Delete un-seen mesh with Blender
The fastest way I can think of which works for the cube case is:


Select part of the outer cube (a single vert will do)
Press CtrlL to select connected vertices
Press CtrlI to invert the selection
Delete.




To delete geometry not visible from the camera:


Enter camera view (Numpad 0)
Ensure you are in solid shading and that Limit selection to visible is enabled
Use border select (B) to select all visible vertices (you may also want to do this with face select enabled to select visible faces too)
Grow the selection (Numpad +)
Delete.




From the camera, there isn't much indication that there are missing faces. Note however that shadows and reflections will be affected.